Is it allowed for a woman to travel without a male relative?

Answer:

In the Name of Allah, the Most Gracious, the Most Merciful.

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It is not permissible for a woman to travel the distance of 77 kilometres or more without a male mahram. Even for the purpose of performing obligatory Hajj it is prohibited for a woman to travel 77 km or more without a male mahram, even if she will be accompanied by other women who will have male mahrams with them. Consider the following hadith:

IbnUmar (RadiyallaahuAnhu) narrates that the Messenger (sallallaahualaihiwasallam) said, “A woman must not travel (the distance of) three days except with a mahram” (Bukhari and Muslim)

Note that the distance of three days equals to approximately 77 kilometres. Therefore it will not be permissible for a woman to travel the distance of 77 kilometres or more without a mahram even if it will only take her a few hours or less to travel this distance (such as in a car or on an airplane).

As for a woman to travel less than the distance of 77 kilometres without a male mahram, it will be permissible only if there is a need for her to do so and there is no fear of fitna. If there is any fear of fitna, it will not be permissible.